{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "569d620b-882a-4d90-a82a-e0c2bb85de9d",
   "metadata": {},
   "source": [
    "\n",
    "姚端正、周国全、贾俊基《数学物理方法》第四版P.275\n",
    "\n",
    "伽辽金法重解例题3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e9220533-845d-4da3-88cf-4e204859b2e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *  # 导入sympy 包中所有的函数\n",
    "x, c0, c1, lamd = symbols('x c0 c1 lambda') # 自定义符号变量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "81a5c4fa-ff42-41c2-ba96-ca44ec677482",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = x*(x-1)*(c0+c1*x)  # 定义试探解，带入泛函并积分\n",
    "Phi = integrate(diff(y,x)**2,(x, 0, 1)) - lamd* integrate(y**2,(x, 0, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "80cd5009-4a79-49dc-9f95-8e97a7e92d55",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{c_{0}^{2}}{3} + \\frac{c_{0} c_{1}}{3} + \\frac{2 c_{1}^{2}}{15} - \\lambda \\left(\\frac{c_{0}^{2}}{30} + \\frac{c_{0} c_{1}}{30} + \\frac{c_{1}^{2}}{105}\\right)$"
      ],
      "text/plain": [
       "c0**2/3 + c0*c1/3 + 2*c1**2/15 - lambda*(c0**2/30 + c0*c1/30 + c1**2/105)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Phi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "25edbd4e-f5cc-4198-9adc-727b92971e53",
   "metadata": {},
   "outputs": [],
   "source": [
    "eq0 = diff(Phi,c0) # 泛函对参数c0求导\n",
    "eq1 = diff(Phi,c1) # 泛函对参数c1求导\n",
    "matrix_c = zeros(2) # 定义2*2零矩阵,用来存储系数的行列式矩阵\n",
    "c = [c0, c1] # 存储系数\n",
    "eqs = [eq0, eq1] # 存储方程\n",
    "for i in [0, 1]: # 计算行系数的列式矩阵\n",
    "    for j in [0, 1]: # 展开方程并获取c_j 项的系数\n",
    "        matrix_c[i, j] = expand(eqs[i]).coeff(c[j]) # 存储c_j 项的系数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8cde541b-f8e3-4b99-9c4e-dfa60244ed66",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{2 c_{0}}{3} + \\frac{c_{1}}{3} - \\lambda \\left(\\frac{c_{0}}{15} + \\frac{c_{1}}{30}\\right)$"
      ],
      "text/plain": [
       "2*c0/3 + c1/3 - lambda*(c0/15 + c1/30)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "69f46e53-7489-42ea-988c-46b5bed6d127",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{c_{0}}{3} + \\frac{4 c_{1}}{15} - \\lambda \\left(\\frac{c_{0}}{30} + \\frac{2 c_{1}}{105}\\right)$"
      ],
      "text/plain": [
       "c0/3 + 4*c1/15 - lambda*(c0/30 + 2*c1/105)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "19071805-db55-4ac0-b6d1-99449c30a5e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{2}{3} - \\frac{\\lambda}{15} & \\frac{1}{3} - \\frac{\\lambda}{30}\\\\\\frac{1}{3} - \\frac{\\lambda}{30} & \\frac{4}{15} - \\frac{2 \\lambda}{105}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[2/3 - lambda/15,     1/3 - lambda/30],\n",
       "[1/3 - lambda/30, 4/15 - 2*lambda/105]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4b7aea0c-06b2-4aec-a70b-83b5fa415006",
   "metadata": {},
   "outputs": [],
   "source": [
    "sol_lamd = solve(matrix_c.det(), lamd) # 求解本征值，存储到sol_lamd中．\n",
    "condition = integrate(y*y, (x, 0, 1)) - 1 # 归一化条件方程．\n",
    "# 把第一个本征值带入eq0, eq1和归一化条件方程中求 c0,c1的值，存储到sol_1．\n",
    "sol_1 = solve([eq0.subs(lamd, sol_lamd[0]),eq1.subs(lamd, sol_lamd[0]), condition], c0,c1)\n",
    "# 把第二个本征值带入eq0, eq1和归一化条件方程中求 c0, c1的值，存储到sol_２中．\n",
    "sol_2 = solve([eq0.subs(lamd, sol_lamd[1]),eq1.subs(lamd, sol_lamd[1]), condition], c0,c1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1bf60508-e940-4180-86eb-dcfe781257aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[10, 42]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol_lamd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2805e586-4b89-4da4-8641-9284c575db05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-sqrt(30), 0), (sqrt(30), 0)]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol_１"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "920c44c9-da68-42c3-90df-c6788b8986c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{c_{0}^{2}}{30} + \\frac{c_{0} c_{1}}{30} + \\frac{c_{1}^{2}}{105} - 1$"
      ],
      "text/plain": [
       "c0**2/30 + c0*c1/30 + c1**2/105 - 1"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "condition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f5f452d0-820a-46ce-927b-22cb3c1e44eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-sqrt(210), 2*sqrt(210)), (sqrt(210), -2*sqrt(210))]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol_２ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "6ef2fbce-3548-4085-897c-716e5217dd7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1f14ca52ad0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(y.subs([(c0,sol_1 [0][0]), (c1,sol_1 [0][1])]),sqrt(2) *sin(pi* x),(x,0,1),ylabel='y(x)', legend=True)\n",
    "\n",
    "#fig1.save('fig1.png',dpi=100)\n",
    "#plot.savefig('xxx.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "21b0d17d-aef0-4327-b326-c47f59d3bc22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1f14ca7cf10>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(y.subs([(c0,sol_2 [0][0]),(c1,sol_2 [0][1])]),sqrt(2) *sin(2*pi* x),(x,0,1),legend=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "13120c2f-2c4c-4c9f-a458-092f4e64d535",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 350x262.5 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scienceplots # 导入'science'画图模块\n",
    "plt.style.use('science') # 采用'science'画图模块\n",
    "fig, ax = plt.subplots() # 建立画布\n",
    "x = np.linspace(0,1,100) # x轴点数\n",
    "y1 = -np.sqrt(30)*x*(x-1) # 近似解\n",
    "y2 = np.sqrt(2) *np.sin(np.pi* x) # 精确解\n",
    "ax.plot(x,y1,linewidth = '0.7',label=r'Approximate solution',color = 'k',linestyle='--') \n",
    "ax.plot(x,y2,linewidth = '0.7',label=r'Exact solution',color = 'k') \n",
    "ax.set_xlabel('$x$') # 设置横坐标名称\n",
    "ax.set_ylabel('$y(x)$') # 设置总坐标名称\n",
    "ax.spines['right'].set_visible(False) # 不显示右边框\n",
    "ax.spines['top'].set_visible(False) # 不显示上边框\n",
    "ax.legend() # 显示标签\n",
    "visible_ticks = { # 设定参数以不显示上和右刻度\n",
    "   \"top\": False,\n",
    "   \"right\": False\n",
    "}\n",
    "ax.tick_params(axis=\"both\", which=\"both\", **visible_ticks) # 去处上和右刻度\n",
    "fig.savefig('Ritz_fig1.png',dpi=600) # 保存图片\n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b17e30d6-6c73-4520-bafd-c65475c1d028",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle -14.4913767461894$"
      ],
      "text/plain": [
       "-14.4913767461894"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N(sol_2[0][0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cb870bd2-86b8-4a00-a3b7-07c2939177d9",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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